ADVANCED: Randomization

GVPT399F: Power, Politics, and Data

Randomization

  • Last session, we randomly assigned 1,000 hypothetical people to two different groups

  • Testing whether randomization helps us create two roughly identical groups prior to treatment

  • You now have a lot of the R code needed to replicate that analysis

Creating our group of 1,000 people

Imagine we have a group of 1,000 individuals. We know the following about them:

  • Height

  • Weight

  • Eye colour

Creating our group of 1,000 people

group_df <- tibble(
  id = 1:1000,
  height = rnorm(1000, 170, 6),
  weight = rnorm(1000, 80, 10),
  eye_colour = sample(c("Blue", "Green", "Brown", "Grey"), 
                      1000, 
                      replace = T)
)

group_df
# A tibble: 1,000 × 4
      id height weight eye_colour
   <int>  <dbl>  <dbl> <chr>     
 1     1   172.   91.7 Green     
 2     2   161.   49.2 Brown     
 3     3   174.   64.1 Grey      
 4     4   164.   74.6 Grey      
 5     5   177.   74.0 Blue      
 6     6   164.   74.8 Blue      
 7     7   166.   84.6 Grey      
 8     8   171.   69.7 Grey      
 9     9   163.   84.8 Green     
10    10   172.   74.0 Blue      
# ℹ 990 more rows

The Normal distribution

ggplot() + 
  geom_density(aes(x = rnorm(n = 1e6, mean = 0, sd = 1))) + 
  theme_minimal()

Random sampling from the Normal distribution

I can take a random sample of n values from a Normal distribution centered at some mean with a specific standard deviation.

  • By default, rnorm() takes a mean of 0 and a standard deviation of 1

  • The following code takes 1,000 random samples from that default Normal distribution

Random sampling from the Normal distribution

rnorm(n = 1000, mean = 0, sd = 1)
   [1]  0.0999385550  0.5527024978 -0.7789031176 -0.1756609143 -2.4791644381
   [6] -1.1127582962  0.6466594309  1.8661261425  0.9176713461  0.4200431117
  [11]  1.1653439471 -0.9335688519  0.9422364599  1.3261605574  0.4801023973
  [16] -0.8478657807 -0.6511132550  1.0816288335 -0.6198677569 -0.6049497599
  [21]  0.2565688873 -1.1594897057 -1.3284865873 -1.4525044374 -0.9762516094
  [26] -0.6468209278 -0.0388196807  0.5167769881 -0.2736533683  0.6517871459
  [31] -1.4548507316  0.6836322735  0.0784148477 -0.8521368669 -0.8366204332
  [36] -0.1301893353 -1.8590221744 -0.8518246510  0.7377490422 -0.8387897577
  [41]  0.3572777261  0.3885708720 -0.2149761217  0.1867636859 -0.2246883255
  [46] -0.3364675498  0.3008649943  0.3351095879 -0.6353895994 -0.0055053818
  [51] -1.0140472336  0.7785094373  1.4027643114 -1.1287119816  0.8556901106
  [56]  1.5849901549 -0.6278046464  0.1851227759 -0.2618091853 -1.4426152681
  [61]  0.2373096206  0.3682529506  0.2700678069 -2.1223576162 -0.1602976508
  [66] -0.8400880408  0.6652432911 -0.9403005877  0.9428635653  0.0844176033
  [71] -3.4799405209  2.2992798220  0.8566559081  0.5905349112 -1.3028936976
  [76] -0.5227303988  1.0103796708 -0.9240229089  0.7305224004  0.0948083546
  [81]  1.0096142228 -0.4605559046 -0.0449350263 -0.1737706906  0.2661312563
  [86]  0.5392020544  0.2218412590 -0.4313964178  1.6906234955 -0.8072247337
  [91] -1.4018070173  0.0589713589 -0.1531696522  0.4786804558  0.2895670485
  [96] -1.2245069094 -0.6802242950  2.1378949170 -0.5333534586  0.4597222077
 [101] -0.2610313433  0.1918025497  0.1329569529 -0.3132016518  1.1374247924
 [106]  1.4472605095  1.6646066009  1.7704090705 -0.4327056658  0.1918787101
 [111] -0.9174081537 -0.8325672333 -1.7174929844 -0.6777422633 -2.5269405405
 [116] -1.2748352610 -0.9759487184  0.8033765342  0.9446858099  0.7149267960
 [121]  1.5410539175 -1.4129310819 -0.2004918550 -1.2762546395 -0.9982532566
 [126]  0.3845917445  0.6553400527 -1.8918844820  1.7107875714  0.5741873244
 [131]  0.3684313408  1.1299296158 -1.4435989325 -1.2546156052 -1.0078550143
 [136] -0.4182101097 -0.2371778096 -1.4480406294  1.0530593826 -0.8791492429
 [141]  1.3757136432  0.8940240414 -1.8799282782 -0.0389806538  0.4140705996
 [146]  0.6298318674  1.5044063192 -0.4558015092 -1.1172408413 -0.7971617196
 [151]  0.3980940979  0.5118919001  0.5857625204  0.6663853130  0.2398399615
 [156]  0.2876502412  0.6071658523  0.6273030847  0.2185118992 -1.8421175080
 [161]  0.8556799737 -0.0290564566 -0.4148615539  1.9007090346 -1.9923818225
 [166] -0.5138866463  1.9869833036 -0.9980326159  1.3924587804 -1.1867535686
 [171]  0.4044859786  0.6163271132  0.3847249083 -0.4197582378  1.2898632248
 [176] -0.7996107306  1.1497183063  1.4003517724  0.7212684313 -1.1511683287
 [181]  0.2218905028 -0.2332486754 -1.3629998285 -1.2634762302 -0.5541606186
 [186]  1.0217032167  0.4195791569  1.8244328411 -0.5682254099  0.3862382740
 [191]  0.4295069367  0.4927773670  0.2907380142 -0.5945454437 -0.0441685531
 [196]  0.1097399489 -1.3228930948 -2.0407874298 -1.2660832958  1.6094095624
 [201]  0.7184931922  0.2876496409 -0.3032697889  0.0791064453  0.0524574721
 [206] -0.3636784158  0.8091096437 -0.7006345382  1.2729305982  0.5655385447
 [211] -0.8049805531  1.1238395648 -1.6246272277 -1.7814998902 -0.4539621742
 [216]  1.6153979978 -0.9218671208 -1.4388891634 -1.4830586021 -0.1464553275
 [221] -0.2657106308  1.5756760493 -0.6222468431  0.8072067390 -0.3972297665
 [226] -2.3774056707  0.4969926303  0.9585397374 -0.1246928779 -0.3816871985
 [231]  0.5953561244 -0.1612027780  0.6305112510 -0.4276357230 -0.8870376005
 [236]  0.3382484936  1.3437565082  0.0665846285  0.5233321970 -0.2069165648
 [241]  1.3940656442  1.1011276657  1.2757277241 -1.0437606074  0.3869475745
 [246] -1.5147624642 -0.9831020825  1.0808964584 -0.0979930985  0.1981141083
 [251] -0.8649630532 -1.7926144116  1.3547204330 -0.3594232180  0.6783775068
 [256] -0.0092592604 -0.2662938161 -1.6219706147  0.8143971386  0.6316454196
 [261]  0.0211187488 -1.4181701835 -1.5476303599  0.2536468934  1.0050908746
 [266] -0.8776236054  0.9160736864 -0.7050925821  1.3756252588  0.5284968114
 [271]  0.0664205285 -0.9966187145  0.1403174972  0.4730241477  1.3539603710
 [276] -0.8898644543 -0.0757762252 -0.9680807349 -1.4736655390 -0.0051400009
 [281]  1.1181438857  0.1699523452 -1.0121784908 -0.3602845885 -1.9456049237
 [286]  1.7675946251 -2.1135902858 -0.7560840169  0.4606923419 -0.7208728524
 [291]  0.1135708143 -1.7934111441 -0.3557956844 -0.8955615291 -0.4508609243
 [296] -0.8239902919 -0.7829403920  0.0252603586 -0.5246752610 -0.4340808089
 [301] -0.9663162301 -0.9291075561 -0.5852715241 -0.7805390976  0.2092418091
 [306] -1.2549146265 -0.8124937770  0.2140200361  0.3849627377  0.8187834209
 [311] -0.8350355642  0.5658479382  1.0998854427  0.9652906664 -1.1102331354
 [316] -0.5851989384  1.0740784331 -0.6945716943  0.7637460233  0.1991893651
 [321] -0.6205506154  0.2442854667  0.5746669519 -0.8417988778 -1.0460147979
 [326] -0.1307458628  1.5022800737  0.0350281900 -0.3842745204 -0.9888122180
 [331] -0.1570044020  0.7330839334 -0.0084021025  0.0881010715  0.9872755051
 [336] -0.2493276360  0.2395761319 -0.7146062625  0.4662256531 -1.9264993141
 [341] -0.1906850895 -0.1590355319  0.7484029905 -0.9840193265  0.4728889907
 [346]  0.1629279341 -1.8064338513 -0.1995547690 -1.5145536013 -1.4304228636
 [351] -0.2791975915 -0.9813383195  0.8834544955 -0.1628697497  0.7244455882
 [356] -0.2286508219 -0.1949378892 -0.7479584809 -0.8217744112 -0.6714046139
 [361]  0.6162492300 -0.2040721084 -3.4312277247  0.5202340095 -0.3926670649
 [366] -0.9153557151 -1.2838940430  0.1889727479 -0.7065969752  0.6894472089
 [371] -0.2712978731 -0.3218036778  0.0869991079 -1.6861502148  0.9225512929
 [376] -0.0965380435 -0.5885739713 -0.9357619902 -0.6548249366  0.5645898406
 [381]  0.0172580383 -0.5333523931 -1.0030728245 -1.7844395650  1.5850860836
 [386] -0.1608832276 -1.3978329799  0.2806625319  0.8594429489 -0.4003594576
 [391]  1.1007183955 -0.1527911328 -1.4653540623  0.8002401361 -0.8435519848
 [396] -1.3508726309 -1.9522134018  0.9640833973  0.4193532685  1.0836849429
 [401]  0.5620248290  0.1149805142 -0.5514282304  0.1032249383  0.5260251985
 [406] -0.0720891378 -0.7035634754  0.2569692169  1.2262640382 -0.5810744995
 [411] -1.4070461936 -0.2858497593  0.6616937049  0.4395938339 -0.0917061980
 [416]  0.4284326307 -0.4256063835  0.0290532552 -0.6070702527  0.2124729810
 [421] -0.5136550517  0.2554785110 -0.0865994939  1.1454668150  0.7998078660
 [426] -0.8868280246  0.3575356188  0.4816921110 -0.0120508469 -0.0429047320
 [431] -0.2482055168 -0.1564514060 -0.6826054363 -1.6696054091  0.5063760782
 [436]  0.6024481733 -1.1034221951 -0.3887503740 -2.1939575753 -0.7930104043
 [441]  0.6674817051  1.2930487301 -0.8719125001  0.1115041553  0.1983434815
 [446] -0.7129504481  0.0587248973  0.4565875854 -0.5340913149  0.7920968440
 [451] -0.6401056980  0.2863133405 -0.1862728470  0.3036704962  0.5478112541
 [456]  0.8317529361 -0.0690163721 -0.0543396254  1.7646574366 -0.1879147374
 [461] -1.4392769294 -0.9409462727  0.1573338939  0.2757192873 -1.1480665072
 [466] -1.2689965271 -0.2714443263 -2.2498669077  0.0971492036 -0.3341234379
 [471]  1.7207952358 -0.7366755597  0.5279124330  1.7125667154  0.2538917959
 [476]  1.0500798078 -0.1932391929  0.1429179153  0.8201521613  1.9422683238
 [481] -0.4424313171  0.6522795629 -1.8428498017 -0.6194993488 -1.7583000809
 [486] -1.2774680067 -0.0747214159  0.0229066916  2.0765205353  2.7711020412
 [491]  0.7765899810  2.6551793897 -0.1417518016  0.2216769036  0.6638468360
 [496]  1.1724513552 -0.2188825635 -0.3286297174  0.1177715133  0.0231303717
 [501] -1.9376441494  2.0681358422  0.4019749095  1.0053498510 -0.2081508525
 [506] -0.5801273870  0.1368379247  0.6114898492 -1.6736918938 -0.8938055230
 [511]  0.5320552442 -0.8409404742 -0.3931874109 -0.4846642324 -0.5488158207
 [516] -0.6372971097  0.7120925641  1.4913728563  1.1904367668 -1.7059960644
 [521]  0.9703618148  3.2175619122 -0.3710251459  0.7350812602 -0.3311396225
 [526] -0.6067601895 -0.8114742236 -0.2473845215 -0.1066266165  0.0008259628
 [531] -1.3206858614 -1.2281863872 -0.0296090696  2.0398995756 -0.8884755291
 [536]  0.6432823974 -1.3465628311  1.6268734845 -1.1169016969 -1.0355446050
 [541]  0.0401650510  0.5741813042 -0.5985627471 -1.8812209712 -0.0809143002
 [546] -2.1208926831 -1.9031945597  0.7954969078  0.4297962694 -1.3600871623
 [551] -1.9803317179  0.6078225972  0.6761863239  0.1070690580 -0.0800851664
 [556] -1.0154504823  0.0390434329 -0.4815942779  1.1851326952 -0.0903616798
 [561] -0.6004103185 -0.1199704174 -0.5511539931 -0.7529450316 -1.5603373399
 [566]  0.6973866041  0.1351705789 -0.2609589787  0.6569208678  1.0338564540
 [571] -0.2754048745  1.0916043033 -0.2938288385 -0.1151483097 -0.9952159515
 [576] -0.2340232450  2.6700263547 -1.9154822336  1.5879220300  1.5374746730
 [581] -1.7636790707  1.0691816709  2.1057200700 -0.2925507018 -0.9659339475
 [586]  1.2200843228 -0.1790980800 -0.4816981600 -0.1983428185 -1.8703250672
 [591]  0.8201436656 -1.3540359139 -1.8257767644  1.2389732835  0.1133799329
 [596]  1.0293506385 -0.7866580338  0.2332838752  0.3058906002  1.2678075056
 [601]  0.5667883380  1.2919548768 -0.9853186953 -0.5816214001 -1.1613788715
 [606]  0.2691391193  0.5712854994 -0.0353740709 -1.0144202832 -0.2050795441
 [611] -0.4672954137 -0.2615072937 -1.0676799230 -0.0444739226  0.4117320914
 [616]  0.7554859830 -1.1846906672  0.5513149249 -0.9176443174  0.2338061998
 [621]  0.2668588850 -0.9335712580  1.5775289834 -0.8706215379 -0.5783230599
 [626]  0.7335923482 -0.6787625511 -1.4588583155 -0.6471931933 -0.1887567548
 [631] -0.1750492339 -0.2892141690  1.9185080989  0.4830577631  1.2015175490
 [636]  0.9809958552  0.2507080548 -0.3873583692  1.7994623714  0.0518662704
 [641]  0.9603013098 -0.7585081192  0.4420065607 -1.3283637696 -0.2204256977
 [646]  0.6519203944 -0.6665820452  0.1574579316 -0.3796320246 -1.0586429007
 [651] -1.4895610647 -0.7908909224 -0.1179535758 -0.3295870952 -0.6906965694
 [656] -0.0228659385  0.5498944454  1.8864002349 -0.3775058556  0.3869468037
 [661]  0.1589848362 -0.8037102904  0.1462819542  0.5616519228  1.6189777132
 [666] -0.6558063805 -0.1554986856  0.8061644764 -0.5073396608  0.4651483820
 [671]  0.5299632077  0.6016250888  0.7939728158  0.1038367456 -0.0859219001
 [676]  0.4590453059 -0.8421172322 -0.6290888757  0.3848062965  0.2840114373
 [681]  1.3064124381  1.2749681693 -0.9721937450  0.4531298324  1.5363476530
 [686]  1.9656024726 -0.0536490814  1.4650086995 -0.5464643843  0.1529238494
 [691] -1.6962707349  0.3404563251 -2.2508025724  0.5263551391  0.7848880498
 [696]  0.1782197004  1.0681866317  0.4701337336  0.7599194121 -0.1712835180
 [701] -0.9561426098  1.0292594352  0.5658732222 -0.5316647163 -0.2955720730
 [706]  0.1867703355  1.5078052443 -1.1280097915  1.7037703077  0.3145254247
 [711]  0.4476684228 -0.2283129256  1.5765219748  0.8857384060  0.3835487422
 [716]  0.7973853559 -1.1529436740 -0.8699768516 -0.8077868368 -0.7042021137
 [721] -1.1722683976 -0.8938308914 -1.0270469919  1.6266238073  1.1206769778
 [726] -0.9422053067 -0.5309476475  0.9090961485 -2.0139173306 -1.1976331924
 [731]  0.8335896808 -1.3725074323 -0.6289234766 -1.2901946286 -1.3324050612
 [736] -0.7746064161  0.0702150363 -0.7601096100  0.1855728959 -0.5416579784
 [741] -0.4075651138  0.7697075661 -0.6351475055  0.1720319495 -1.7130171068
 [746] -0.3710577199 -0.9618658670  1.2456079268 -0.2628545382  1.9995843242
 [751]  1.0373406694  0.4830968400 -0.3570441629  0.9350630284  1.0432426729
 [756]  1.5972352154 -0.6088199281 -0.6644990599  0.8578476795 -1.3364662346
 [761]  0.0542268960  1.3142513194  0.9827152397 -0.8694145102 -2.1957426503
 [766] -0.5016465576  0.3488509358 -0.6153455217 -1.1695688502  0.0493848566
 [771]  0.4624926713  1.4205146011  1.0472636155 -0.9896304469 -0.3997480532
 [776] -0.2340809800 -2.5120671157 -0.5300536287  0.3855878287 -0.1982847724
 [781] -2.2908548308  1.7093795035 -0.9263673542  1.3248145907  0.6027834506
 [786]  0.4959249730  1.0819397728  0.6884002690 -0.6667738486 -1.1917405205
 [791]  0.1395405390  0.0313114499  0.3613395745 -0.1011620077 -0.1692588930
 [796] -1.1245562266  2.3328967628  0.1624603947  0.1049123246 -0.8879295303
 [801]  2.1314918753  0.1081747625  0.8262557654 -0.3037626924 -0.4085148451
 [806] -0.2226462193 -0.7708156853  1.3848212938  0.5939839550 -0.5717405218
 [811] -1.9079586024  0.5230677689  0.6068783865  0.8668994109 -0.9596296709
 [816] -0.7729157325 -0.4519478338  1.1177776066  0.9344931858 -0.2889778563
 [821] -1.0792877523 -1.1762805493  0.3484441802 -0.0241779342 -0.2500805473
 [826] -0.8617330182  0.7956938731 -0.3447477560  1.0438735788  2.6625112625
 [831] -1.5460705331 -0.5844856119  0.5292906566  0.9709059079  0.3122711364
 [836] -0.3676510913 -0.3723782341 -1.5482778722  0.0237613039  0.2456770845
 [841]  1.1314993348 -0.5404563993  0.2617320999 -0.7191301599 -0.4891796901
 [846] -0.4357413049 -0.9038379786  0.5630366917  0.8928142390  0.1762598885
 [851] -1.2568281743 -0.0353147973  0.4186596800  0.1334466945  1.5742294191
 [856]  0.6093846826 -0.8683082262  0.1269261184 -0.5696287463 -0.9310201074
 [861] -0.1521545004  1.7942726334  0.2226819358 -0.0524859136 -0.4253876516
 [866]  1.2613210222 -0.3700160886 -1.3514473779  2.2297755488  0.2827902881
 [871] -0.4112070182 -1.0548538415  0.1903368365 -0.5469141524  0.9701556465
 [876] -0.6464497270  0.8657658885 -1.0691834808 -1.3854618481 -0.9528062573
 [881]  0.9903138203 -1.3586606177 -1.1943727137 -1.2092158297  0.1020346153
 [886] -1.1383286987 -0.5804245753 -1.6013201423 -1.7340270225 -0.0970538130
 [891] -0.5197142945  1.6316208246  0.2277787803 -0.6255520457 -0.8069703615
 [896]  0.8614201268 -1.3953218046 -0.7188242857  0.3642497207  1.4112718361
 [901]  0.8899319596  1.1568332647  2.4583518943  1.0469216205  2.3432745698
 [906] -0.1761792109 -0.3227993750 -0.4834840369  1.5338574777 -4.0121498013
 [911]  0.9461821042  0.3474819456  0.9963940751  1.1888174427  0.6464727818
 [916]  0.5350104918  0.9704066986 -0.2073437416  0.7184958635  0.6570896220
 [921]  2.2257986709  0.0611686189  1.8643146875 -1.1487361143  0.0854731334
 [926]  1.5162728661 -0.7819765271  0.5276977355  0.5826648289  0.8061938957
 [931]  0.6656661948  0.6329711319 -2.5618889177 -0.5963978665 -0.1522974341
 [936] -0.7332463108  0.3266842043  1.0568738703 -0.4656569082 -0.0210913332
 [941] -0.3489804349 -0.1705811318  0.3917415869 -0.3016817167 -0.7868254417
 [946] -1.3005891568  1.2556679619 -0.9201784716  0.9702014853  0.1976708816
 [951]  0.4897556500  0.0304393235 -0.2497496941  0.1253635475  1.0690336285
 [956] -0.5928865641  0.1812305139  0.8162409617  1.2618637535 -1.5850511297
 [961] -0.4682959593 -0.9447203000  0.4398930444 -1.7945873986  0.0799402517
 [966]  1.2311845720 -0.3290181222  0.2184265793 -0.6177916618 -0.5005666078
 [971] -1.1122818906  0.6201490825  0.0790423756 -0.3458012761 -0.0762138969
 [976]  0.1325975938  0.2810106002  0.4613856635 -1.3674897215 -0.1332614293
 [981]  0.0066938156 -0.0807159485 -2.3267037462  0.3812021724  0.3107076783
 [986]  0.0101479804  0.7895009628 -0.2171852222  2.3456127819 -0.0642654219
 [991] -0.4454808373  0.6244519769 -0.2239376676  0.1035587900  0.1213560083
 [996]  1.7173279770  2.2774565979 -0.3525469374 -1.1708536127 -1.0861849947

Random assignment using the Binomial Distribution

Remember, we then randomly assigned them to one of two groups: A or B.

  • I used random draws from the Binomial (read: binary or two) distribution to do this.

Random assignment using the Binomial Distribution

rbinom(n = 1000, size = 1, prob = 0.5)
   [1] 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 0 0 1 0 1 1 1 1 0 0 1 0 0 1 0 1 0 1 1 1 1
  [38] 0 1 1 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 1 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0
  [75] 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 1
 [112] 0 1 1 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 1 0 1 1 0 1 1 0 0 0 1 0 0 1 1 1 0 1
 [149] 0 0 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 0 1 0 1 0 1 1 0 1
 [186] 0 0 0 1 1 1 1 1 0 0 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 0 1 0 1 0 1 1 1 0 0 0 1
 [223] 1 0 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 0 1 1 1 0 0 0
 [260] 1 1 0 1 1 0 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 0 1 0 0
 [297] 0 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0
 [334] 0 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 1 0
 [371] 0 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 1 0 0 1 0 1
 [408] 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 0
 [445] 0 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 1 1 1 1 0 0 0 0
 [482] 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 1
 [519] 0 1 1 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 1 1 0 0
 [556] 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 0 1
 [593] 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 1 1
 [630] 0 0 1 0 0 1 1 1 1 0 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 0 1 1
 [667] 0 1 1 1 1 0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0
 [704] 1 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0
 [741] 0 0 0 1 1 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 1 1 1 0
 [778] 0 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 1 1 0
 [815] 1 0 0 1 1 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 0 1 0 1 0
 [852] 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 0 1
 [889] 0 0 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 1 1 1 0 1
 [926] 1 1 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0
 [963] 0 1 1 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 1
[1000] 1

The Binomial Distribution

ggplot() + 
  geom_bar(aes(x = rbinom(n = 1e6, size = 1, prob = 0.5))) + 
  theme_minimal()

Assigning our people with mutate()

assigned_group <- group_df |> 
  mutate(
    group = rbinom(1000, 1, 0.5),
    group = factor(group, labels = c("A", "B"))
  )

assigned_group
# A tibble: 1,000 × 5
      id height weight eye_colour group
   <int>  <dbl>  <dbl> <chr>      <fct>
 1     1   172.   91.7 Green      B    
 2     2   161.   49.2 Brown      A    
 3     3   174.   64.1 Grey       B    
 4     4   164.   74.6 Grey       A    
 5     5   177.   74.0 Blue       B    
 6     6   164.   74.8 Blue       A    
 7     7   166.   84.6 Grey       A    
 8     8   171.   69.7 Grey       A    
 9     9   163.   84.8 Green      B    
10    10   172.   74.0 Blue       A    
# ℹ 990 more rows

Comparing our two groups

Comparing our two groups

Comparing our two groups